A posteriori error estimates for mixed approximations of degenerate elliptic problems

Abstract

We consider the Raviart-Thomas mixed finite element approximation of non-uniform elliptic problems of the form −div(a∇u)=f where a=a(x) is in the Muckenhoupt class A2. We introduce an error estimator based on a local post-processing and prove its efficiency and reliability, generalizing to the degenerate case the theory developed in [24]. Finally, we present some numerical computations for a model problem showing the good behaviour of an adaptive procedure based on our estimator.